Artificial ambiance processing system

ABSTRACT

An apparatus and method simulates more accurately the natural statistics of a physical reverberation process. A new filter design is provided having a comb shaped group delay. Gain minimums at a plurality of frequencies are combined with a delay line to create a constant reverberation time independent of frequency while allowing for temporal spreading. In addition, the connection topology between the plurality of energy transmission networks is temporally randomized to facilitate energy distribution within the reverberation apparatus. Both the temporal and spectral responses are actively changed on each iteration of the energy recirculation. By making the response have a high echo density and a lack of spectral coloration in the decay, the illusion of a natural process is enhanced.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of, and claims priority to, U.S.application Ser. No. 11/331,370, filed on Jan. 12, 2006, titledARTIFICIAL AMBIANCE PROCESSING SYSTEM, which is a divisional of, andclaims priority to, U.S. patent application Ser. No. 09/922,816, filedon Aug. 6, 2001, titled ARTIFICIAL AMBIANCE PROCESSING SYSTEM, whichclaims priority under 35 U.S.C. §119(e) to U.S. Provisional PatentApplication No. 60/226,884, filed Aug. 22, 2000, titled ARTIFICIALAMBIANCE PROCESSING SYSTEMS, all applications of which are incorporatedby reference in this application in their entirety.

RELATED APPLICATION

This application claims priority to U.S. provisional application No.60/226,884, Attorney docket number 5764, entitled “Artificial AmbianceProcessing System, by Barry A. Blesser, filed Aug. 22, 2000.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to artificial reverberation and ambiance systemsthat create the illusion of real acoustic spaces, and more specificallyto systems for simulating more accurately the natural statistics of aphysical reverberation process.

2. Background of the Invention

In an acoustic space, the sound travels from the source to the listenervia many different paths. The direct path, referred to as the “dry”signal, corresponds to the signal of an anechoic space, an outdoorperformance, or a close microphone. The indirect path, referred to asthe “wet” signal, bounces off the walls or other surfaces multiple timesand appears at the listener delayed, attenuated, and spectrallymodified. The process continues with more and more reflections arrivingat the listener later and later. Thus, all reverberation processes canbe thought of as a rapidly increasing series of reflections or echoes.In audio signal processing, “ambiance” is the general sense of creatingan illusion of a space. “Reverberation” is more specifically the decayprocess once the process has become so complex that only a statisticalrepresentation is useful. Ambiance includes reverberation and spatiallocation of the listener. Since the earliest days of radio broadcastingand recorded music, the need for artificial reverberation and spatialambiance has been well known. When a microphone is placed close to aperformer to avoid picking up background noise, very little of theenvironmental reflections appear in the signal. Reverberation, createdby an artificial system, is added to the microphone signal to recreatethe perception of the acoustic space.

Typically, signal processing systems often fail to accurately duplicatenatural acoustics for both practical and theoretical reasons. The echopattern or impulse response is extremely complex and only the early partof the process can be characterized in detail. Impulse responsemeasurement decays into the noise level because the amount of sourceenergy is limited to a fraction of the atmospheric pressure. Averagingcannot be used because of the lack of thermal equilibrium, which causesminor changes in the speed of sound. For the same reason, frequencyresponse measurements never reach a stable steady state. Also, thecomputational burden on ray tracing algorithms grows exponentially.Moreover, the detailed echo pattern is different for each seat in everyspace and the physics of a 3-dimensional space is fundamentallydifferent from the 1-dimension properties of signal processing. Along agiven axis, the speed of sound varies as a function of the angularorientation, giving a sound wave two extra degrees of freedom. In asignal processing system, signals travel at a fixed rate through alldelay lines. Fortunately, the physical complexity of the process doesnot match the human's ability to perceive minor differences. As aresult, there is a large body of research that teaches which attributesare perceptible.

Because of these factors, artificial systems attempt to create theperceptual illusion of a real acoustic space without trying to bephysical simulations thereof. Large spaces have been better analyzed interms of statistics rather than in terms of an explicit impulseresponse. When an artificial system has similar statistics the illusionis good; when those statistics differ, the illusion is weak. However,the prior art shows a tendency to either use an artistic or purelymathematical approach. There is very little prior work that provides aformalism that can relate the statistical properties of an artificialsystem to the perceptually relevant properties of acoustic performancespaces.

The current generation of artificial reverberation systems is based on afew digital signal processing primitives including delay lines,multipliers, and adders. From these primitives, more complex elementsare created. A comb filter, that is implemented with a delay line havingfeedback of less than 1, derives its name from the fact that thefrequency response is comb shaped. An allpass filter, which is a combfilter combined with a feedforward path, has a flat frequency response,hence the name allpass. An energy transmission network, which iscomposed of a large delay line, holds and transmits the energy betweendifferent parts of the system. These transmission networks are directlyanalogous to a linear path through cubic sections of air in a realacoustic space, which also hold and transmit acoustic energy. Otherelements, such as filters, are added to provide the more subtleattributes such as high frequency absorption of wall surfaces and theair itself.

Historically, reverberation systems were based on one of two basictopologies. One of these topologies uses a multiplicity of comb filtersfed in parallel from a series of allpass filters. The other topologyuses a single large loop composed of a multiplicity of delays, lowpassfilters, and allpass filters. About 15 years ago, these structures wererepresented as static mixers using a matrix notation. Not only can thematrix notation represent all of the basic reverberation topologies byselecting appropriate numbers, but the notation can also be used tocreate other topologies as long as the numbers are constrained to a setof mathematical rules. The matrix column vectors should have unitymagnitude and each of these vectors should be orthogonal to all theothers. Any set of numbers that satisfies these rules is the to be aunitary orthogonal matrix. However, there are an infinity of matrixnumbers that satisfies the mathematical rules. The prior art does notteach a selection criterion. Constraining the mixer coefficients to beconsistent with these rules is necessary, but not sufficient, to createa high quality reverberation system because the rules ignore additionalperceptual issues that are unrelated to the mathematical formalisms. Thevarious necessary perceptual optimizations often conflict with oneanother; optimizing one, while de-optimizing the other.

Another problem of the prior art is that it is limited to using arelatively small number of energy transmission networks because of theirhigh economic burden. It is essentially impossible to fill thesenetworks uniformly because statistical averaging requires a large numberof such elements. In a real acoustic space, the energy density becomesuniform after the reverberation process has continued for a modestamount of time. Artificial systems show a much weaker tendency toproduce a uniform energy distribution and, hence, often produce energyperiodicity in the reverberation, which is perceptible to the listener.

Because there are different classes of defects in reverberators, it isuseful to first consider two extreme classes of sound: broadband pulsesand narrow band continuous signals. The former is typical of a pluck ona guitar or a bang of wood blocks, while the latter is typical of aflute, organ and other instruments that have a long steady state. Mostmusic falls between these two cases. In discussing reverberationssystems, professional audio engineers will often refer to the systembehavior when excited either by an impulse or by a steady statesinewave, representing the two extreme cases. A defective reverberationsystem will show undesirable properties with one or both of these cases.Typically, an audio engineer first looks for the perceptual smoothnessof the reverberation tail as the dominant quality criterion. Secondly,he also looks for spectral coloration in the tail. Does the spectrum ofthe reverberation have the same spectral content as the original? Theuntrained listener does not detect these defects explicitly but has thesense that the reverberation is not quite right. Professional soundengineers are, however, very sensitive to even the most minor defects.Experts in the field can catalog dozens of critical cases that form thetool chest for evaluation. The fundamental difficulty in creating theillusion of reverberation derives from the fact that optimizing one setof properties often de-optimizes others.

The prior art has a strong proclivity to describe artificialreverberation systems as being a complex linear and time-invariantfilter. The linearity property dictates that scaling the input by afactor will typically scale the output by the same factor. Thetime-invariant property dictates that shifting the input in time willtypically shift the output by the same amount. A similar approach hasbeen rejected when applied to a large acoustic space, such as a concerthall, because it is very misleading and unproductive. It is useful onlyin the degenerate example of a small and rectangular shaped acousticspace. A concert hall might easily have more than 100,000 resonances and100,000 discrete echoes. Scientists therefore often use a statisticalnotation that talks about the frequency response in terms of itsaverage, standard deviation, slope rates, etc. The reverberation decayis described in terms of the spectrum of the amplitude envelope andspectrum of the phase changes. An impulse response can be described interms of the spectrum of energy variation within a 1 msec. time window.The scientific literature shows that there have been some notablesuccesses in mapping the statistical metrics to the perceptualproperties.

In contrast, artificial systems are generally very limited in theircomplexity. Audio engineers have traditionally not described thereverberation response in terms of statistics but have stayed with thedeterministic notion of a linear, time-invariant construct. Somereverberation designers abandon all structured methods and resort to apurely artistic creation process. Because artificial systems aregenerally built out of less than 20 network modules with only some 50free parameters, there is no obvious method to incorporate a statisticalapproach into the design process. There are simply not enough degrees offreedom. Consider, for example, how the resonance density behaves whenexcited with a narrow band musical note. A large concert hall can easilyhave a density of well over 10 resonance per Hz, whereas an artificialsystem might have only 0.3 resonances per Hz. When the density isextremely high, many excited resonances contribute to the responseresulting in a random envelope and phase response. With only 2 excitedresonances, the envelope will have a characteristic beat tone at afrequency equal to the difference between the two resonances, whichsounds very unnatural. This problem has been intuitively understood buthas not been extensively studied. Historically, the solution hasinvolved some kind of isolated parameter randomization. For example, adelay can be slowly changed, or a delay output can be panned betweenrandom values. All of these methods have limited utility and somenegative artifacts. Very few methods work within the main recirculationprocessing because any artifact, such as needle generation, will alsorecirculate. The prior art has not solved these problems. The prior artgenerally ignores the subject of statistical randomization, even thoughit is critically important.

SUMMARY

This invention improves artificial reverberation and ambiance processingsystems by providing a mechanism to create the appropriate randomenvelope and phase statistics in the output signal. The inventive systemuses two new building blocks: (1) a notchpass filter as a constituentpart of an energy dispersive transmission network and (2) an energypreserving modulation mixer in a recirculation topology, both of whichcan be used separately, but which reinforce each other when usedtogether. In a typical embodiment, the modulation mixer creates feedbackby randomly routing the output energy from a plurality of transmissionnetworks back to their respective inputs. As the energy recirculates,both the networks and the mixer repeatedly change the audio in astatistically desirable way thereby avoiding the more typical structuredperiodicity and beat tones typical of prior art systems.

The notchpass filter may comprise a delay line with both feedback andfeedforward appropriately adjusted to have gain minimums at the sameplurality of frequencies as the group delay maximums. The notchpassfilter is then combined with a second, longer delay line and anattenuator to form an energy dispersive transmission network. Thisnetwork has the dual desirable properties of both increasing the echodensity for pulse signals and differentially delaying the spectralcomponents for steady state signals. By appropriate selection of thenetwork parameters, the reverberation time can be made independent offrequency even though the filter's gain, by itself, is not spectrallyconstant. Having a constant reverberation time may be critical becauseany spectral component with a longer decay time would remain audiblewhile all other components had decayed. It is desirable for the spectralbalance of the reverberation decay to remain constant and to be the sameas the input audio to avoid coloration, a situation where a few tonescompletely dominate. Because most reverberation topologies are based onrecirculation, the energy dispersive transmission network will operaterepeatedly on the previous signals as they circulate around the feedbackloop. On each iteration, the echo density will be dramatically increasedand the spectral components will be further spread in time.Perceptually, the constantly changing recirculated signals take on arandom quality without any periodicity.

An energy preserving modulation mixer may also be used to create n audiooutput signals, called an audio output vector, from n audio inputsignals, called the audio input vector, using a transformation by whicheach output signal is composed of a changing weighted sum of the inputsignals. The transformation mapping between the audio input vector andthe audio output vector may be continuously changed such that the amountof a given audio input signal that appears in a given audio outputsignal is not static. The transformation, driven by a set of mrandomizer signals, is constrained so that the energy in the audiooutput vector is typically the same as the energy the audio inputvector. The modulation mixer's n audio outputs feeds a set of n energydispersive transmission networks and their respective n outputs feed themixer's n audio inputs, thus creating an energy recirculation loop.Because the transformation may be continuously changing, the energy froma given network is distributed differently to each of the other networkson each iteration. The modulation mixer does not increase or decreasethe energy in the audio vectors; hence the reverberation time is notinfluenced by the time varying transformation. The m randomizer signalsserve to randomize the interconnections between the plurality of energydispersive transmission networks rather just randomizing a singleparameter. The reverberation response can be made to have naturalstatistics by the appropriate choice of the m randomizer signals. With astatic mixer, the reverberation would have a characteristic beatenvelope equal to the difference between neighboring resonances. Suchundesirable property is avoided by randomization of the topology, orequivalently by randomizing the resonances, but without changing theenergy decay process. Randomly moving resonances emulate the highresonance densities of large acoustic spaces.

Since the invention is based on randomization, the total system energyis the only attribute that remains relevant as the individual signal'sphase and amplitude are continuously modified during recirculation.Achieving a linear decay process at the output is equivalent to havingthe total system energy decay at a logarithmic rate. The energypreserving modulation mixer does not change the total energy in thesystem but does change the distribution among the plurality of networks.Each energy transmission network reduces the energy at a constant ratebut does change its signal's phase and amplitude. Both mechanisms have arandom quality to create natural statistics at the final output.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention can be better understood with reference to the followingdrawings and description. The components in the figures are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention. Moreover, in the figures, likereference numerals designate corresponding parts throughout thedifferent views. In the drawing:

FIG. 1 is a block diagram illustrating an implementation of areverberation system using a notchpass filter and an energy transmissionnetwork;

FIG. 2 is a block diagram illustrating an implementation of a notchpassfilter where the module for implementing the filter poles is distinctfrom the module to implement the filter zeros;

FIG. 3 is a block diagram illustrating an alternate implementation of anotchpass filter with the inner loop producing the filter poles and anouter feedforward path producing the filter zeros;

FIG. 4 is a block diagram illustrating an alternate implementation of anotchpass filter with an inner feedforward path to produce the filterzeros and an outer feedback loop to produce the filter poles;

FIGS. 5-6 are graphs illustrating the group delay and amplitude,respectively, as a function of frequency, for the inventive notchpassfilter used in a reverberation topology system;

FIG. 7. is a block diagram illustrating a reverberator with four energydispersive transmission networks connected with feedback using a mixerto combine the n outputs with the m inputs to create the n sourcesignals to feed the four network inputs;

FIG. 8 is a block diagram illustrating a reverberator with a pluralityof energy dispersive transmission networks in parallel;

FIG. 9 is a block diagram illustrating a a reverberator with a pluralityof energy dispersive transmission networks in a single large loop;

FIG. 10 is a block diagram illustrating a notchpass filter modified toallow for a frequency dependent notch depth, that may be needed toimplement a reverberation time as a function of frequency;

FIG. 11 is an s-plane representation of the pole-zero pattern for theinventive notchpass filter designed to work with an energy transmissionnetwork that has a flat frequency response;

FIG. 12 is an s-plane representation illustrating a modification of thereal part of the line of zeros for various filters that might be used inthe energy transmission network;

FIG. 13 is an s-plane representation illustrating a modification of thereal part of the line of zeros for various filters that might be used inthe energy transmission network;

FIG. 14 is a block diagram illustrating a 2×2 energy conservingmodulation mixer that can be used by itself or as a building block tocreate higher order modulation mixers;

FIG. 15 is a block diagram illustrating four sets of 2×2 energyconserving modulation mixers connected to form a 4×4 version, with agenerator to create the modulation signals;

FIG. 16 is a graph illustrating samples of generator signals that can beused to drive a modulation mixer to produce random topology changes;

FIG. 17 is a block diagram illustrating additional detail of a 4×4energy preserving modulator having sixteen modulators and obtaining acoefficient generator from the four modulation signals;

FIG. 18 is a graph illustrating the modulation signals with each signalhaving a different rate, but only one signal changing at each instant oftime, and each signal stopping when hitting a threshold corresponding to45, 135, 225 or 315 degrees;

FIGS. 19-21 collectively form a block diagram illustrating areverberation system using the dispersive energy transmission networksand the randomizing modulation mixer of the present invention;

FIG. 20 is a block diagram illustrating a reverberation system using thedispersive energy transmission networks and the randomizing modulationmixer;

FIG. 21 is a block diagram illustrating a reverberation system using thedispersive energy transmission networks and the randomizing modulationmixer; and

FIG. 22 is a block diagram illustrating a 4×4 modulation mixer with anaudio output vector supplied to loudspeakers, which in conjunction withan acoustic space and microphones, function as an energy transmissionnetwork.

DETAILED DESCRIPTION

This invention provides a system capable of actively creating therequired random temporal and spectral statistics of naturalreverberation for audio signals, especially speech and music. An impulseand a sinewave are generally used to illustrate the behavior of theinvention because they span the complete range of interesting audiocases. The former exists only in short instant of time but has a verybroad spectrum; the latter exists for a long time but has a very narrowspectrum. The invention allows for the simultaneous optimization of boththe impulse and sinewave response. The prior art puts these twooptimizations in conflict. An unstructured high echo density no longerproduces spectral coloration and vice versa. These conclusions may applyto a vast number of reverberation topologies and architectures.

Most reverberation systems contain a multiplicity of long delay lineswith attenuation, called energy transmission networks. They hold andtransmit the acoustic energy. Except for the case of a very long serieschain of energy transmission networks, the networks are configured torecirculate energy via one or more feedback paths. In order to achieve auniform system reverberation time, all energy transmission networksshould have the same ratio of attenuation, when expressed in dB, to itsmatching delay time. System reverberation time, abbreviated RT, isdefined as the time to decay 60 dB. A 100 msec. delay line having anattenuation of 3 dB has the same decay rate as a 200 msec. line with 6dB of attenuation. Both decay at a rate corresponding to a 2 second RT.Since both the delay length and the attenuation are constant,independent of frequency, the resulting ratio is also constant. Thus,all frequencies typically have the same RT.

This invention modifies the standard energy transmission networks toalso produce dispersion. Frequency components are each delayed by adifferent amounts (spectral spreading) and a single impulse istransformed into a plurality of impulses (temporal spreading). Becausethese energy transmission networks are embedded in a feedback topology,the temporal and spectral dispersion will modify the signal on eachiteration. The continuous change achieves the requirement of preventingcoherent patterns in the decay process. Typically, a comb filter addedto a delay line will create dispersion. However, the comb filter'sfrequency response has a grossly non-uniform amplitude and group delayshape. An allpass filter could be used instead to create a flatfrequency response, but its group delay would still have a comb filtershape. These structures cannot be used, because they will result in anunacceptable comb shaped RT as a function of frequency. These structuresproduce a high level of spectral coloration. Only a few frequenciesdominate with their much longer RT.

To achieve the requirement of a spectrally flat RT while addingdispersion, this invention creates a new structure, called a notchpassfilter. It is built from a comb filter with feedforward, but has theadded property that its frequency response is the mirror image of itsgroup delay response. The gain is made to have periodic minimums at thesame frequencies as the group delay maximums. Because both the gainminimums and delay maximums can be controlled independently, the energytransmission network's RT can be made to be independent of frequency.The notchpass filter in combination with a standard energy transmissionnetwork becomes a new building block, an energy dispersive transmissionnetwork, that may replace standard energy transmission networks inreverberation topologies.

For example, a notchpass filter may have a 10 msec. delay line thatproduces group delay peaks at 100, 200, 300, 400, etc. Hz, and groupdelay minimums at 50, 150, 250, 350, etc. Hz. A typical notchpass filtergroup delay is shown in FIG. 5. Assume that the delay of a standardenergy transmission network has a value of 97 msec. and assume that thenotchpass filter has a group delay of 53 msec. and 3 msec. at themaximums and minimums, respectively. To make all frequencies have thesame 2 second RT, parameters are selected so that the base attenuationis 3 dB and the notchpass filter gain minimums produce an additional 1.5dB. A typical notch pass gain is shown in FIG. 6. A 100 Hz spectralcomponent experiences a composite delay of 150 msec. with a compositeattenuation of 4.5 dB, while the 50 Hz component experiences a shorter100 msec. delay but with a smaller 3 dB of attenuation. Both spectralcomponents have the same decay rate. However, assuming that the signalhas a flat frequency response in each network would be wrong. Rather,the RT may be made to have no frequency dependence. It is necessary onlyto have a flat spectrum in the reverberation output. Internal signalsare irrelevant. All spectral components in the output should decay atthe same rate. Historically, prior art systems achieved the flatspectrum by making both attenuation and gain independent of frequency.However, this prevents the desirable property of dispersion from beingincluded within the recirculation. This invention makes themproportional.

When the energy dispersive transmission networks are used in areverberation system, each spectral component experiences a differentreverberation process because the group delays are different for eachmusical overtone. Each overtone, being at a different frequency, has itsown a unique recirculation pattern. On repeated iterations, eachovertone is time shifted relative to the others by the difference ingroup delays at the overtone frequencies. The phase coherence in thedecay is completely removed. Impulse signals have the same property. Oneeach iteration, the signal is dispersed anew by the notchpass filter.Furthermore, the echo density at the output increases dramatically aswould happen in a natural process because there are k impulse in thenotchpass filter output for each input impulse. On the next iteration,each of those k impulse itself produces k more impulses, etc. Eventhough there is no active randomization, the invention allows each partof the reverberation to be very different from every other part in bothits time and spectral structure. RT is defined as the time for thesignal to decay by approximately 60 dB. Thus, it is often determined byextrapolating the decay rate, which is the change in signal per unittime with units of dB per second.

The previous discussion illustrated the invention under the assumptionthat having a spectrally flat decay rate was ideal. In practice, it ismore desirable to have a longer RT at low frequencies than at highfrequencies. A modest change in RT duplicates real acoustics because thehigher frequencies experience more absorption from air attenuation andsurface reflections. The desired RT frequency response generally has adownward slope with, for example, values of 3 seconds at 100 Hz, and 1.5seconds at 5 kHz being typical. In a standard energy transmissionnetwork, a simple filter was added to make the main attenuation have thesame kind of gradual increase as a function of frequency. The inventionmay include a matching compensation filter within the notchpass filterso that the depth of its gain minimums also increase with frequency.System RT now has the desired shape, a gradual decrease with increasingfrequency, but without any of the comb shape had the notchpass filternot been modified with a matching compensation filter.

There is a direct analogy between an energy transmission network in anartificial system and a volume of air in a natural acoustic space sincethey both hold and transmit acoustic energy. Because sound travels in3-dimensions, the energy in a given volume of air can chaotically moveto any of its 6 neighboring regions: above, below, left, right, front,and back. Conceptually, the physical space can be thought of as havingthousands of individual cubic energy storage volumes. As the naturalreverberation process continues, the energy gets uniformly distributedto all of them.

Many prior art systems have achieved the equivalent complex connectionbetween a large number of energy transmission networks by using a 2 or 3dimensional mesh topology. Such systems remain laboratory curiositiesbecause of their extremely high compute cost. Economic limitationsgenerally require that only a few energy transmission networks be used.It is also well known that good quality reverberation may require aresonance density of at least 3 per Hz, implying a total delay in allenergy transmission networks of 3 seconds. By having four delay networksof 750 msec. each to incorporate 3 seconds of delay, it would take avery long time for the reverberation process to distribute energyuniformly to such large delay lines.

This invention achieves the equivalent statistics using only a modestnumber of energy transmission networks with only a modest amount oftotal delay. The smaller delays allows for rapid filling while the smallnumber of networks satisfies the economic requirements. This inventionprovides a methodology for time randomization of the topologicalconnections between energy transmission networks. Its is well known thata static mixer based on the unitary orthogonal matrix properties canprovide a energy distribution but the statistics only work when thereare a large number of energy transmission networks. The invention solvesthese problems by randomly changing the topological connectionsrepresented by the modulation mixer. Without such randomization, andwith a limited amount of total delay, the decay envelope will have avery disturbing periodic beat. That frequency of the beat tone will beequal to the difference between neighboring resonances.

The need for randomizing in artificial reverberation systems has beenwell known but the techniques currently in use are either insufficientor have undesirable properties. Random delay is very difficult toimplement in a digital signal processing environment because theinterpolation between taps produces a high rapid time amplitudemodulation of high frequency signals. Interpolation artifacts limit theuse of the changing delays to be mostly outside of the majorrecirculation loop. This invention provides a new scheme for producingthe desired statistics by changing the nature of the recirculationrather than by changing isolated delay values.

A multiplier can be used for two distinct purposes when one of theinputs is an audio signal. The second input can be a fixed number, whichproduces a linear scaling of the audio signal in the form of anattenuator or amplifier, or the second input can be another timechanging signal, which creates a modulation process. While implementedin a similar fashion, they serve fundamentally different functions. Anattenuator is not the same as an amplitude modulator. In this invention,each of the fixed constants in a mixer is replaced with a correspondingmodulator. That modulator is driven by a process that createscontinuously changing coefficients. When the process is correctlydesigned, the mixer continuously changes the topological connectionsbetween the energy transmission networks without producing anyartifacts.

In one embodiment of the invention, the n² fixed coefficient multipliersof the static mixer with are replaced with corresponding modulators eachhaving a second time varying input signal. As a black box, the completemodulation mixer should be considered as having n audio input signals,called the audio input vector, n audio output signals, called the audiooutput vector, and n² coefficient modulation input signals, called thecoefficient modulation vector. The invention contains an additionalnetwork to drive the coefficient modulation vector so that themodulation signals are constrained to satisfy the energy conservationproperty of the audio output vector. When the energy in the audio outputvector is constrained to be the same as the energy in the audio inputvector, the modulation mixer can be used in the feedback recirculationtopology of a reverberator containing a plurality of energy transmissionnetworks. The modulation signals can be random, pseudo-random, orperiodic but within the constraint.

The invention functions to randomize the topology of the recirculation.At different times, each of the energy transmission networks feeds adifferent amount of its energy to the other networks, including itself.Since these ratios change with time, the connections are thusrandomized. At one instant of time, network 1 might feed 20% of itsenergy to itself, 40% to network 2, 10% to network 3, and 30% to network4. At another instant of time, network 1 might feed 50% to itself, 5% tonetwork 2, 25% to network 3, and 20% to network 4. As long as thedistribution energy sums to a constant, namely 100%, such a structurewill produce smooth reverberation decay. A large energy burst in oneenergy transmission network is relatively quickly distributed to theother networks.

The two parts of the invention are closely related in that theillustrative embodiment contains a modulation mixer, that is energypreserving. The modulation mixer is also combined with one or moreenergy transmission networks, each of which has a uniform energy decayrate. As a result, the reverberation decays uniformly; it is notdegraded by either of the two processes. Neither the modulation processof the mixer nor the dispersion of the energy transmission networksproduces spectral coloration of the reverberation time; but they bothbreak up repeating patterns.

An implementation of the reverberation apparatus, as shown in FIG. 1,may be based on the single energy dispersive transmission network 31,comprising notchpass filter 26 and standard energy transmission network29, embedded in a single feedback loop 32. The output of the energydispersive transmission network 31 is coupled back to input adder 20 toform the main feedback loop 32. Feedback loop 32 recirculates the energythat enters from input 19 with a gradual decay determine by thecoefficient gRT input of multiplier 28 and by the gain of notchpassfilter 26. In the illustrative embodiment, delay 27 may be relativelylong, ranging from 30 to 300 msec., while delay 23 may be typically setto a value of about 25% of delay 27. The composite delay of notchpassfilter 26 and energy transmission network 29 determines how long ittakes the energy to recirculate.

Notchpass filter 26 comprises a feedback loop around delay 23,multiplier 24 and adder 21. The amount of dispersion and the peak groupdelay is determined by the value of gP input of multiplier 24. Thecloser to 1.0, the larger the value. The feedforward path via multiplier22 with coefficient gZ allows for controlling the gain minimum at thosefrequencies where the group delay peaks. FIGS. 5 and 6 illustrate thegroup delay and amplitude respectively as function of frequency fortypical values of gZ and gP. The composite delay around the mainfeedback loop 32 comprises delay 27 and the group delay notchpass 26,while the composite gain around loop 32 comprises gRT and the gain ofnotchpass 26. Generally, reverberation time around a recirculating delayline is defined by Equation (1) below

$\begin{matrix}{{RT} = \frac{{- 3}*T}{\log \; g}} & (1)\end{matrix}$

where g is the composite gain and T is the composite delay. Given anytwo parameters, Equation (1) can be used to compute the third. Theminimum group delay in the notchpass filter is defined by Equation 2below

$\begin{matrix}{T_{\min} = {{\frac{1 - g^{2}}{1 + g^{2} + {2\; g}}*T_{ap}} = {\frac{1 - g}{1 + g}*T_{ap}}}} & (2)\end{matrix}$

where T_(ap) is the delay line in the notchpass filter and g is theaverage of gP and gZ, as defined in Equation (7). Similarly, the maximumgroup delay is defined by

$\begin{matrix}{T_{\max} = {{\frac{1 - g^{2}}{1 + g^{2} - {2\; g}}*T_{ap}} = {\frac{1 + g}{1 - g}*T_{ap}}}} & (3)\end{matrix}$

Equations (2) and (3) represent the frequencies where the delay producesan out of phase condition and an in-phase condition, respectively.Notice that on a linear scale, Equation (3) dominates because T_(max)rapidly goes to infinity as g approaches 1.0. At the frequency where thegroup delay is a maximum, the minimum gain is defined by Equation 4below

$\begin{matrix}{G_{\min} = \frac{1 - g_{Z}}{1 - g_{P}}} & (4)\end{matrix}$

where gZ is the gain coefficient for the zeros and gP is the gaincoefficient for the poles. Similarly, the maximum gain is defined byEquation 5 below

$\begin{matrix}{G_{\max} = \frac{1 + g_{Z}}{1 + g_{P}}} & (5)\end{matrix}$

at a frequency where the group delay is a minimum. When the energystorage network, having a gain of gRT, is combined with the notchpassfilter, the composite g is equal to gRT*G_(min) and gRT*G_(max) for theminimum and maximum, respectively. Similarly the composite delay isT_(RT)+T_(min) and T_(RT)+T_(max) for the same two cases where T_(RT) isthe delay of the energy storage network. Since both the composite gain gand composite delay T are a function of frequency, the values of gP andgZ are selected so that RT is remains constant. Effectively, Equation(1) is solved twice, once at the in-phase frequency and once at the outof phase frequency.

The values of delay 27, delay 23, gain gRT, and g are design choiceswith a set of reasonable values being 100 msec, 25 msec, 0.7, and 0.5,respectively. The equations are then used to compute the values of gPand gZ. Equations (2) and (3) evaluate directly since all of theindependent parameters are given. The differences between gP and gZ isapproximately given by Equation (6) below

$\begin{matrix}{{g_{Z} - g_{P}} = {\left( {1 - g} \right)\left( {1 - {\frac{1}{g_{RT}}*10^{\frac{{- 3}{({T_{\max} + T_{RT}})}}{RT}}}} \right)}} & (6)\end{matrix}$

which can be used to determine gP and gZ when equation (6) is added orsubtracted from the definition of g by Equation (7) below

g _(Z) +g _(P)=2*g  (7)

A numerically exact solution can be obtained by using any number ofmathematical tools such as Mathcad software, commercially available fromMathSoft, Inc., Cambridge, Mass. 02142, but Equation (6) is almostperfect because G_(max) is both very close to 1 and not very sensitiveto changes in the gZ and gP values. An alternative solution methodrequires the computation to be done twice, initially assuming G_(max) is1, and then using the actual G_(max) based on the previously computedvalues of gP and gZ. When these values are used in the system of FIG. 1,energy will recirculate and decay at a constant rate for allfrequencies. Those frequencies having a longer delay will also have ahigher attenuation.

The same result will be achieved if notchpass filter 26 is replaced withany of the alternative implementations shown in FIG. 2-4 or 10. Thenotchpass filter may be implemented as a linear, time-invariant filter,which can be described in terms of its poles and zeros. The location ofthe poles and zeros in the circular Z plane for sampled data systems, orin the rectangular S plane for continuous systems, complete defines theresulting filter. Each of the topologies may have at least twoindependent gains and at least one delay line.

FIG. 2 illustrates an alternative embodiment of the notchpass filter ofFIG. 1. In this embodiment, filter network 44 which implements the polesis separated from filter network 48 that implements the zeros. Theoutput from filter network 44 feeds filter network 48, but the sameresult is achieved if filter network 48 feeds filter network 44. Delays42 and 45 have approximately the same delay values in order to make thedelay maximums coincide with the same frequency of the gain minimums.The multiplier 43 is used to set the pole value gP. Multiplier 46 isused to set the zero value gZ. Adder 41 completes the feedback path forthe poles and adder 47 adds the direct and delayed signals to create thezeros. Note that adder 25 of FIG. 1 and adder 47 are both adding thesame signals.

FIGS. 3 and 4 show alternative implementations of the notchpass filterof FIG. 1. Delays 52 and 63 may have, the same value. Both topologieshave a feedback loop created by multiplier 53 with adder 51 andmultiplier 62 with adder 61. Both have a feedforward path created bymultiplier 64 with adder 65 and multiplier 54 with adder 56. The actualvalues for the multiplier coefficients are shown in terms of the basicpoles location gP and zero location gZ. Of the four implementation shownin FIGS. 1-4, generally the configuration of FIG. 1 is more versatilebut different applications may make the alternative topologies moreefficient.

In the invention, the notchpass filter parameters are adjusted toproduce a group delay and amplitude characteristics shown in FIGS. 5 and6. The group delay may have has a very wide range, often with a maximumto minimum ratio of as much as 25:1. When the notchpass filter's groupdelay is combined with the larger delay of the energy transmissionnetwork, the composite delay variability is greatly reduced. Thenotchpass filter's gain minimums are typically on the order of 0.8 andits maximums may be very slightly above 1.0, with the exact valuesdependent on the parameters. These values are for illustrative purposesonly.

The more general case of feedback using the energy dispersivetransmission networks is shown in FIG. 7 with four such networks 404,405, 406, and 407. The n outputs in signal path 403 are connected tomixer 401 that combines the n signals with one or more of the m inputsin signal path 400 to create the n inputs in signal path 402. The mixeradds and scales one or more of the signals in signal path 403 with oneor more of the inputs in signal path 400 for each signal in signal path402. By changing the nature of the mixer, the connections illustrated inFIGS. 8 and 9 can be created. Typically, mixer 401 is of the energypreserving type.

Applications for the energy dispersive transmission network are shown inFIGS. 8 and 9. These are real reverberation topologies thattraditionally used a standard energy transmission network. Elements76-79 and 92-95 may be implemented with the energy dispersingtransmission network 31 of FIG. 1 or with the modified notchpass filterdesign of FIGS. 2-4 and 10. In FIGS. 8 and 9 the energy dispersivetransmission networks may be of identical design, but with differentparameters. The topologies of FIGS. 8 and 9 both will produce qualityreverberation. The four output channels 72, 73, 74, and 75, for theparallel design, and outputs 96, 97, 98, and 99 for the large loop, caneither feed four loudspeakers or can be mixed to provide a stereophonicor monophonic output. The input is shown as monophonic signal 70 and 90but can be expanded to include provisions for a multiplicity of inputs.These architectures may have other optional pre-processing elements 71and 91, including one or more allpass filters, lowpass filters, etc.

In order to duplicate the gradual decrease in RT with increasingfrequency, a very gentle lowpass filter replaces the gRT coefficient ofmultiplier 28 of FIG. 1. The exact shape of that lowpass may becontrolled by the user, e.g. from the front control panel. Given theadvantages of avoiding a comb shaped response in RT, a matchingfrequency dependence may replace the gZ coefficient of multiplier 22.While somewhat arbitrary, the matching filter is constrained by the setof equations (1) through (7). Such filters have no required topology.

FIG. 10 illustrates an alternative design of a notchpass filter. Filter101 replaces gZ and can be implemented as a standard FIR type (finiteimpulse response) of any odd order. The order is the number of taps. Ifthose coefficients in filter 101 are symmetric, the filter is phaselinear, which can be modeled as a simple delay. Delay 102 may beinserted to match the delay of filter 101. Both signal paths enteringadder 103 may have the same phase. Hence, the filter is equivalent to afrequency dependent gZ. In practice, the delay line in filter 101 anddelay 102 are merged with delay 105 in a single element to savecomputation time and are shown separately for illustrative purposes.

The inventive notchpass filters, regardless of the implementation ortopology, can be described using standard signal processing notations inthe form of the s-plane representation for continuous-time systems, or,in the form of the z-plane representation for discrete time systems. Itis well known that s-plane and z-plane representations are equivalent.It is also well known that a linear, time-invariant filter can beconverted to one of these two representations. The notchpass filtersdescribed herein can be equivalently described either in terms of thes-plane poles and zeros or in terms of a network diagram. In the s-planerepresentation, the poles of the notchpass typically appear on avertical line and are equally spaced along the vertical or imaginaryaxis. The zeroes are also on a line but, unlike the poles which are inthe left half plane, the zeros are in the right half plane. The line ofzeroes is typically closer to the vertical axis than the line of polesin order to achieve the periodic comb-like attenuation of the notchpassfilter. FIGS. 11 to 13 only show the upper two quadrants of the s-placebecause the lower two quadrants are mirror images of the upperquadrants. Poles and zeros appear as complex conjugates of each other,except if there is a single pole and zero at Direct Current.

FIG. 11 illustrates the location of the poles and zeros for a notchpassfilter in accordance with the present invention. The pole line 350contains a sequences of poles with the real part 353 which is determinedby the feedback gP and zero line 351 contains a sequence of zeros withreal part 354. Both poles and zeros are spaced the imaginary frequencydistance 352 that is determined by the size of the delay line. In theillustrative embodiments of the inventive notchpass filter, there istypically a pole with the same imaginary frequency as the correspondingzero. As used herein, especially with reference to the s-planerepresentation of FIGS. 11-13, the term “line” is not limited to astraight line.

When the gRT has been replaced by a filter, and when the notchpass ismodified to take this property into account, the poles or the zeros willtypically no longer be on a straight line. FIG. 12 and FIG. 13illustrate two examples of a bent line of zeros to achieve optimumripple free results. The shape of the bend is determined by the natureof the filter that replaced gRT. Bending the zero line is equivalent tobending the pole line since the attenuation is determined by the ratioof the real part of the zeros to the real part of the poles. Increasingone distance is equivalent to decreasing the other. In FIG. 12, the zeroline distance from the imaginary axis starts at the value of 361 andgradually decreases along line 360. In FIG. 13, the zero line distancestarts at the value of 371, gradually increases, and then decreasesalong line 370.

While optimum ripple free reverberation time is desirable, economicconsiderations may allow more ripple. Such would be the case when gRThad been replaced by a filter, but the line of poles and zeros was leftstraight as shown in FIG. 11. With an optimum design, the comb-likeattenuation ripples illustrated in FIG. 6 are made to vary withfrequency by applying equations (1) to (7) at each frequency. Generally,the frequency changes in RT are sufficiently gentle that these equationonly need be applied at a few select frequencies. With a non-optimizesdesign, the ripple depth may be constant as shown in FIG. 6.

FIG. 14 illustrates a 2×2 modulation mixer 128. Mixer 128 can be used byitself, or can be used as a building block to create higher ordermixers. An input audio vector, composed of audio signals 130 and 131,feeds the four modulators multipliers 139A-C, that are driven by thecoefficient vector 137 to create an audio output vector, composed ofoutput signals 132 and 133. The energy in the audio output vector istypically the same as the energy in the audio input vector as long asthe coefficients are created by network 135. Energy conservation comesfrom the simple trigonometric rule:

sin²+cos²=1

for all angles.

The modulation process comprises modulation multipliers 139A, 139B,139C, and 139D in mixer 138. The randomization signal which appear atinput 134 is created by signal generator 129. Within converter 135 therandomization signal 134 is supplied to trigonometric functions, thatgiven an input value, generate a corresponding function value as theoutput thereof. Such trigonometric outputs serve as the coefficientvector 137 by which the audio input vector is modulated by themodulation mixer 136.

The resulting output audio vector 138 comprises signals 132 and 133. InFIGS. 9-15, circuit paths that cross are not assumed to be connected.

FIG. 15 illustrates a 4×4 modulation mixer 145 using four modulationmixers 140-143, each of which includes a coefficient converter andmodulation mixer, similar to converter 135 and modulation mixer 136,respectively of FIG. 14. Since each basic modulation mixer is energyconserving, pairs of signals can be passed through any number of thedevices. Modulator mixers 140 and 142 each randomize pairs of the inputsignal while modulation mixers 141 and 143 randomize their correspondingoutputs. The input audio vector comprises the four input signals 144A,144B, 144C, and 144D, while the resulting output audio vector comprisessignals 146A, 146B, 146C, and 147D. The four randomization signals 147A,147B, 147C, and 147D are created by generator 144. The approach shown inFIG. 15 is a two-stage implementation. An infinite variety ofconfigurations can be created cascading any number of modulation mixer.A 5^(th) modulation mixers could be added to the outputs, or the 4^(th)mixer removed. The amount and type of randomizing may be left to thedesigners choice. Generally, it is desirable to have as few modulationmixer stagers as possible while still randomizing most or all the audioinput signals. Moreover, by keeping the number of cascading generationsto a small value, there is no build up of modulation sidebands.

FIG. 16 illustrates typical signals 150-153 that may be used to drivethe modulation mixers 140-143 of FIG. 15. In this figure, the inputsignal is viewed as having phase units, namely that the signal runs from0 to 360 degrees and then wraps back to 0. Using a phase wrappingnotation is not a requirement but simplifies the implementation. Indigital signal processing, wrapping can be easily achieved by making thelargest fixed-point digital number correspond to 360 degrees and thesmallest correspond to 0. Since fixed-point digital numbers wrap, phasewrapping happens automatically. Signal 150 is shown having a randomslope that changes at random intervals. Such a signal will result incoefficients that appear to be a sequence of random sinewave segments atdifferent frequencies. Signal 151 is shown as a pure linear phase thatcreates a sinewave coefficient. Signal 152 is shown with a linear

FIG. 17 illustrates the implementation of a 4×4 modulation mixer 125. Aninput vector, comprising audio input signals 110, 111, 112, and 113,feeds the 16 modulators that create an audio output vector comprisingsignals 115, 116, 117, and 118. A modulation vector, comprisingmodulation inputs 121, 122, 123, and 124, provides the basis from whichcoefficients are generated by generator 120. Generator 120 may implementthe two mathematical rules for energy conservation. The magnitude of thevertical coefficient vector should be 1.0 at all times, and the dotproduct of all the vectors with each other, except itself, should be 0.0at all times. The design shown in generator 120 is an expansion of theconnection of 2×2 modulation mixers shown in FIGS. 14 and 15. Asillustrated in FIG. 17, generation of the coefficient values ispartially achieved with trigonometric functions prior to scaling.

FIG. 18 illustrates other modulation signals 160-163. Each of the foursignals shown has a different slope corresponding to a differentfrequency. Only one signal changes at each instant of time and runsuntil hitting the threshold of 45, 135, 225, or 315 degrees. After therunning signal reaches its stopping point, the next signals startchanging. The signal 160 is shown hitting the threshold of 315 degrees,which then results in signal 161 running until 215 degree threshold. Theprocess continues at the reference points of signals 162 and 163. Inthis example, the stop-start algorithm is sequential and follows a fixedorder. The order shown is 1, 2, 3, and 4 with repeat. Alternatively, thestop-start ordering may be random, or the slopes may be random. Themajor advantage of the sequential generator is that only one modulationprocess is active at a given time. The start-stop approach not onlyreduces the computation burden but allows the spectral spreading to becontrolled explicitly. In FIG. 15, the modulation products of 140 add tothose of 141 if both modulation inputs are changing at the same time. Inan alternative implementation, the modulation signals 160-163 besub-sampled, and can run at half or a quarter of the rate of the audiosignal since they are low frequency signal.

The major advantage of the start-stop algorithm is that it avoids adefect when using periodic or random signals as the source of themodulation coefficients. A mixer produces the maximum amount of energyspreading when all of the coefficients have a value of +/−0.5; eachenergy transmission network feeds 25% of its energy to each network. Themixer produces the least amount of mixing when all of the four diagonalterms are 1.0 and all off-diagonal terms are 0.0. Each network feeds100% of its energy to itself and none to the others. Because of therandomization, the mixer will occasionally exist in one state andoccasionally in the other. A given musical note may be perceiveddifferently in these two extreme cases. The start-stop algorithm solvesthis problem because the four thresholds all correspond to coefficientswith a magnitude of 0.5. Only the running signal is not at one of thesethresholds.

The nature of the phase randomization signals is critical to theoperation of the invention. If they are changing too slowly, there willbe no perceived randomization of the reverberation topology. If they arechanging too rapidly, there will undesirable modulation artifactsintroduced, i.e. new spectral side-bands are created. The higher themodulation frequency, the more spectral spreading. The amplitude andphase of natural reverberation also has also has spectrum spreading. Therandomization signals should be selected to match the spreading thatwould appear in natural reverberation, which is a function of the RT.For typical reverberation times, the spreading corresponds to a spectrumbetween 0.3 to 3 Hz. Hence, the randomizer should be adjusted to producea similar amount of spectral spreading. Phase randomization signals maygenerally be in the range from 0.3 to 3.0 Hz, to make the reverberationtail have an unstructured and non-periodic personality.

FIGS. 19, 20 and 21 show an alternative embodiment containing both theenergy dispersive transmission networks, described previously withreference to FIGS. 1-10, and the random modulation mixer, describedpreviously with reference to FIGS. 14-18. Stereo audio input signals arefed into lines 248 and 249 where they are diffused by allpass networks242 and 243, respectively, each of which has two allpass filterdiffusors. The outputs of networks 242 and 243, respectively, feed delaylines 244 and 245 to allow for unreverberated delayed signals to be feddirectly to the output. Lines L, M, N, O, P and Q appear directly in theoutput summations 251 and 255. This kind of preprocessing is typical ofreverberation system, representing a simulation of the individual earlyreflections. The choice of preprocessing is based on the type ofacoustic space and the location of the listener. In the earlyreflections, the statistics process has not yet begun. The randomizationmodulation mixer 241 is part of the main recirculation loop thatincludes four sections of processing. The four sections comprise theenergy dispersive transmission networks 200, 210, 220, and 230, as wellas filtering sections 201, 211, 221, and 231. Networks 200, 210, 220,and 230 may be implemented with the energy dispersing transmissionnetwork 31 of FIG. 1 or with the modified notchpass filter design ofFIGS. 2-4 and 10. Filtering sections 201, 211, 221, and 231 mayimplement a frequency dependent reverberation time by changing the gRTfor high and low frequencies. The feedback path 202, 212, 222, and 232around a unit delay of a respective filter section implement a 1^(st)order lowpass filter that serves to reduce the feedback of highfrequencies. The feedback path 204, 214, 224, and 234 around anotherunit delay of a respective filter section create a lowpass filter atvery low frequencies, typically 200 Hz. By adjusting gains 203, 213,223, and 233, the amount of low frequency RT can be adjusted separatelyfrom the amount of high frequency RT. Each of the main delay lines 200,210, 220 and 230 in the energy dispersive transmission networks is shownwith four taps, each feeding the output summation networks 251 and 255.These summation networks represent the fully reverberated signals fromthe recirculation networks. Finally, the ratio of reverberation to dryinput signal is adjustable by mixers 252 and 256 to form the stereooutput signals 253 and 257.

Any of the signal processing circuits and, including the inventivenotchpass filter, energy dispersive transmission networks, andmodulation mixer shown in FIGS. 1-22 may be implemented using acommercially available Digital Signal Processor (DSP) integratedcircuit, such as the Motorola 56004 chip from Motorola, Inc,Schlumberger, Ill., The published programming instructions and libraryroutines for such DSP may be used to construct algorithms which functionaccording to the illustrated signal processing circuits, such algorithmsbeing within the scope of those skilled in the arts in light of thisinvention. Other products with in the Motorola 56000 family of productsmay be similarly used. In addition, DSP product from other manufactures,such as the SHARC Series, commercially available from Analog Devices,Norwood, Mass., the TMS 320 Series, commercially available from TexasInstruments, Dallas, Tex., may be similarly used, or any other availableDSP product may be used to implement this invention.

An application will often have additional processing components insertedat various point, e.g. there may be components of the energy dispersivetransmission network inter-mingled with other functional blocks. In somecases, the functionality is implicit. For example, the main attenuationcan be embedded within the notchpass filter without being explicitlyrepresented. These variations do not change the basic invention but aredesigners implementation preferences.

The actual parameters in the embodiment are a few strong function of theapplication. Is the system to simulate a symphony hall, a bathroom, atrain station, a small chamber or an opera hall? Is the listener sittingclose to the stage or in the 3^(rd) balcony? Is the music classical,popular or hard rock? The number of questions is so large, and each ofthe answers determines the optimum settings for the network parameters.Furthermore, economic considerations determine the amount of signalprocessing that can be used. The design shown in FIG. 20 has fouroutputs of delay taps on each of the four delay sections. Should therebe more processing resources, more taps may be added. With lessresources, three taps might be used instead of four.

In the preferred embodiment, additional optimization can be performed toachieve better performance. Smoothness in the reverberation decay can beimproved if the energy in each 1 msec. interval is essentially the sameas the neighboring intervals. To use this approach, the proposed designis simulated in a computer with starting values for all parameters. Animpulse is entered into the input and the complete output is analyzed asa sequence of 1 msec. windows. This represents the average energy oramplitude in the output envelop. A metric such as the peak variation inenvelop or the power in the envelop is applied to the output to create afigure of merit. The process is repeated a large number of times witheach iteration using slightly different design parameters. This is knownas a Monte Carlo simulation.

A simple example illustrates the process. Consider having 4 parametersthat need to be optimized and that each parameter can have 3 values. Themiddle value is the starting reference and each of the other valuesrepresents an incremental increase or decrease in that value, forexample, 1% change. Since each of the 4 parameters can each have one ofthree possible values, there are a total of 3⁴, or 81 cases. After thefigure of merit has been computed for each, the optimum is selected asthe new starting reference and the process repeats. One of those 81cases will be more optimum than all the others. Because computers are soinexpensive, a very large system can be so optimized by long computerruns. There are many other equivalent numerical techniques that can beused. The exact technique for finding the optimum is not important. Itis important that the reverberation decay have minimum energy variationsin the envelop over a 1 msec. averaging window. The size of the windowis not critical since it is only an approximation to human hearing.

FIG. 22 illustrates a 4×4 modulation mixer 305 with audio output vector302 feeding four loudspeakers 310, 311, 312 and 313 located in anacoustic space 304, such as concert hall. The four microphones 320, 321,322, and 323 send their signals back to modulation mixer 305 as theaudio input vector 301. The mixer 305 is driven by four randomizersignals 330, 331, 332, and 333 in the modulation vector 300. The audiosource, not shown, may be located inside of acoustic space 304.Alternatively, a prerecorded audio signal can be supplied to theloudspeakers. In this embodiment, the loudspeakers, acoustic space andmicrophones function as an energy transmission network, as analternative those purely electronic implementations described herein.

A software implementation of the above-described embodiments maycomprise a series of computer instructions either fixed on a tangiblemedium, such as a computer readable media, e.g. diskette, CD-ROM, ROM,or fixed disk, or transmittable to a computer system, via a modem orother interface device, such as communications adapter connected to thenetwork over a medium. Such medium can be either a tangible medium,including but not limited to optical or analog communications lines, ormay be implemented with wireless techniques, including but not limitedto microwave, infrared or other transmission techniques. The series ofcomputer instructions embodies all or part of the functionalitypreviously described herein with respect to the invention. Those skilledin the art will appreciate that such computer instructions can bewritten in a number of programming languages for use with many computerarchitectures or operating systems. Further, such instructions may bestored using any memory technology, present or future, including, butnot limited to, semiconductor, magnetic, optical or other memorydevices, or transmitted using any communications technology, present orfuture, including but not limited to optical, infrared, microwave, orother transmission technologies. It is contemplated that such a computerprogram product may be distributed as a removable media withaccompanying printed or electronic documentation, e.g., shrink wrappedsoftware, preloaded with a computer system, e.g., on system ROM or fixeddisk, or distributed from a server or electronic bulletin board over anetwork, e.g., the Internet or World Wide Web.

Although various exemplary embodiments of the invention have beendisclosed, it will be apparent to those skilled in the art that variouschanges and modifications can be made which will achieve some of theadvantages of the invention without departing from the spirit and scopeof the invention. It will be obvious to those reasonably skilled in theart that other components performing the same functions may be suitablysubstituted. Further, the methods of the invention may be achieved ineither all software implementations, using the appropriate processorinstructions, or in hybrid implementations that utilize a combination ofhardware logic and software logic to achieve the same results. Suchmodifications to the inventive concept are intended to be covered by theappended claims.

1. A signal processing system comprising: a first delay module; a firstmultiplier, coupled to the first delay module, capable of creating areal frequency line of poles; and a second multiplier, coupled to thefirst delay module, capable of creating a real frequency of the line ofzeros; where for every pole located left of an imagery y axis in ans-plane representation, there is a corresponding zero in the right halfplane of the s-plane representation at a same imaginary frequency andthe zeros are closer to the imaginary y axis than the poles.
 2. A signalprocessing system comprising: a first delay module capable of creating areal frequency line of poles; and a second delay module capable ofcreating a real frequency of the line of zeros; where for every polelocate left of an imaginary y axis of an s-plane representation, thereis a corresponding zero in the right half plane of the s-planerepresentation at a same imaginary frequency and the zeros are closer tothe imaginary y axis than the poles.
 3. A filter comprising: a delaymodule capable of creating a line of poles and zeros, where for everypole located left of an imaginary y axis in an s-plane representation,there is a corresponding zero in the right half plane of the s-planerepresentation at a same imaginary frequency; and the zeros are closerto the imaginary y axis than the poles.
 4. A filter comprising: a delaymeans for delaying a signal and for creating a line of poles and zeros,where for every pole located left of an imaginary y axis in an s-planerepresentation, there is a corresponding zero in the right half plane ofthe s-plane representation at a same imaginary frequency; and the zerosare closer to the imaginary y axis than the poles.
 5. A signalprocessing system comprising: a first means for delaying a first signaland for creating a line of poles; a second means for delaying a secondsignal and for creating a line of zeros; and where for every polelocated left of an imaginary y axis in an s-plane representation, thereis a corresponding zero in the right half plane of the s-planerepresentation at a same imaginary frequency and where the zeros arecloser of the imaginary y axis than the poles.
 6. A signal processingsystem comprising; a first means for delaying a signal; a secondmultiplier means, coupled to the first means for delaying the signal,for creating a real frequency line of zeros; and where for every polelocated left of an imaginary y axis in an s-plane representation, thereis a corresponding zero in the right half plane of the s-planerepresentation at a same imaginary frequency and where the zeros arecloser to the imaginary y axis than the poles.
 7. An energy dispersivetransmission network, comprising: (A) a notchpass filter means capableof receiving an input signal and generating a first output signals, thenotchpass filter comprising a first delay means for creating a line ofpoles and zeros, where for every pole located left of an imaginary yaxis in an s-plane representation, there is a corresponding zero in theright half plane of the s-plane representation at a same imaginaryfrequency and the zeros are closer to the imaginary y axis than thepoles; (B) a second delay means capable of receiving the first outputsignal generated by the notchpass filter means and generating a secondoutput signal; and (C) a multiplier means for scaling the second outputsignal according to a gain to generate a third output signal, an energydecay rate of the third output signal relative to the input signal beingsubstantially identical at all frequencies.